#lang scheme
(require (prefix-in base: (only-in scheme + /)))
(require "typeclass-units.ss")

;; A class of things for which addition is defined.
(define-signature addable^ (zero +))

;; A class of things for which division is defined.
(define-signature divisible^ (/))
  
;; Standard arithmetic on numbers.
(define-instance (addable^ divisible^) num@
  (define zero 0)
  (define + base:+)
  (define / base:/))

;; Addition over strings is defined as string-append.
(define-instance addable^ string@
  (define zero "")
  (define + string-append))

;; The "+" function is a generic addition operation.
(define-constrained (+ (addable^) => x y)
  (+ x y))
  
((+ num@) 3 4)              ; Adding numbers
((+ string@) "hi " "there") ; Adding strings
  
;; A helper combinator.
(define (flip f) (λ(x y) (f y x)))

;; The definition of the "mean" function requires both addition and division.
(define-constrained (mean (addable^ divisible^) => items)
  (/ (foldl (flip +) zero items) (length items)))
  
;; Computing the mean of a list of numbers.
((mean num@ num@) '(4 5 6))

;; Try giving an incompatible instance of divisible^... doesn't work.
((mean string@ num@) '("what " "is " "an average " "string?"))